Strength and equation of state of boron suboxide from radial x-ray diffraction in a diamond cell under nonhydrostatic compression

Using radial x-ray diffraction techniques together with lattice strain theory, the behavior of boron suboxide (B₆O) was investigated under nonhydrostatic compression to 65.3 GPa in a diamond-anvil cell. The apparent bulk modulus derived from nonhydrostatic compression data varies from 363 GPa to 124 GPa depending on the orientation of the diffraction planes with respect to the loading axis. Measurement of the variation of lattice spacing with angle, ψ, from the loading axis allows the d spacings corresponding to hydrostatic compression to be obtained. The hydrostatic d spacing obtained from a linear fitting to data at 0° and 90° is consistent with direct measurements at the appropriate angle (ψ=54.7°) to within 0.5%, which suggests that even two measurements (ψ=0° and 90°) are sufficient for accurate hydrostatic equation of state determination. The hydrostatic compression data yield a bulk modulus K₀=270±12 GPa and its pressure derivative K₀′ = 1.8±0.3. The ratio of differential stress to shear modulus ranges from 0.021 to 0.095 at pressures of 9.3-65.3 GPa. Together with estimates of the high-pressure shear modulus, a lower bound to the yield strength is 26-30 GPa at the highest pressure. The yield strength of B ₆O is about a factor of 2 larger than for other strong solids such as Al₂O₃. The ratio of yield stress to shear modulus derived from lattice strain theory is also consistent with the result obtained by the analysis of x-ray peak width. This ratio might be a good qualitative indicator of hardness as it reflects the contributions of both plastic and elastic deformation.